Please wait a minute...

Frontiers of Mechanical Engineering

Front. Mech. Eng.    2015, Vol. 10 Issue (3) : 277-286
Fault diagnosis of spur gearbox based on random forest and wavelet packet decomposition
Diego CABRERA1,2,*(),Fernando SANCHO2,René-Vinicio SÁNCHEZ1,Grover ZURITA1,3,Mariela CERRADA1,4,Chuan LI1,5,Rafael E. VÁSQUEZ6
1. Departamento de Ingeniería Mecánica, Universidad Politécnica Salesiana, Cuenca, Ecuador
2. Departamento de Ciencias de la Computación e Inteligencia Artificial, Universidad de Sevilla, España
3. Departamento de Ingeniería Electro-Mecánica, Universidad Privada Boliviana, Cochabamba, Bolivia
4. Departamento de Sistemas de Control, Universidad de Los Andes, Mérida, Venezuela
5. Research Center of System Health Maintenance, Chongqing Technology and Business University, Chongqing 400067, China
6. Facultad de Ingeniería Mecánica, Universidad Pontificia Bolivariana, Medellín, Colombia
Download: PDF(1892 KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

This paper addresses the development of a random forest classifier for the multi-class fault diagnosis in spur gearboxes. The vibration signal’s condition parameters are first extracted by applying the wavelet packet decomposition with multiple mother wavelets, and the coefficients’ energy content for terminal nodes is used as the input feature for the classification problem. Then, a study through the parameters’ space to find the best values for the number of trees and the number of random features is performed. In this way, the best set of mother wavelets for the application is identified and the best features are selected through the internal ranking of the random forest classifier. The results show that the proposed method reached 98.68% in classification accuracy, and high efficiency and robustness in the models.

Keywords fault diagnosis      spur gearbox      wavelet packet decomposition      random forest     
Corresponding Authors: Diego CABRERA   
Online First Date: 09 September 2015    Issue Date: 23 September 2015
 Cite this article:   
Diego CABRERA,Fernando SANCHO,René-Vinicio SÁNCHEZ, et al. Fault diagnosis of spur gearbox based on random forest and wavelet packet decomposition[J]. Front. Mech. Eng., 2015, 10(3): 277-286.
Fig.1  Training process for the RF classifier
Fig.2  Test process for the RF classifier
Fig.3  Configuration of system for failure’s simulation
Fig.4  Feature extraction process. (a) WPD; (b) energy extraction and features vector building
Mother wavelets oob-error Feature’s number Tree’s number
db7 0.0590 12 1901
db7+sym3 0.0419 8 1713
db7+sym3+coif4 0.0410 7 1671
db7+sym3+coif4+bior6.8 0.0390 17 727
db7+sym3+coif4+bior6.8+rbior6.8 0.0438 10 1191
Tab.1  The best selected wavelets and the best model parameters
Fig.5  Curves of training: (a) oob-error for each set of wavelets with variable number of random features; (b) oob-error for the set of the best wavelets for maximum randomness (1), maximum correlation (256) and perfect randomness (17) with a variable number of trees
Fig.6  Selection of features: (a) Importance of features without selection; (b) importance of features with selection; (c) curve of further training to the selection of features
Class 1 2 3 4 5 6 7
1 37 0 0 0 0 0 0
2 0 37 0 0 0 0 0
3 0 3 34 1 0 0 0
4 0 0 2 35 1 0 0
5 0 0 0 0 38 0 0
6 0 0 0 0 0 36 1
7 0 0 0 0 0 0 37
Tab.2  Confusion matrix
Metric Value/%
Accuracy 96.950
Sensibility 97.000
F score 96.975
Tab.3  Classifier’s performance measures
Class 2 3 4 5 6 7
1 100 100 100 100 100 100
2 96.05 100 100 100 100
3 96.3 100 100 100
4 98.68 100 100
5 100 100
6 98.65
Tab.4  AUC individual unit: %
Fig.7  Separation of samples. (a) Location of samples; (b) coordinates eigen-values
1 Walha  L, Fakhfakh  T, Haddar  M. Backlash effect on dynamic analysis of a two-stage spur gear system. Journal of Failure Analysis and Prevention, 2006, 6(3): 60–68
2 Abbes  M S, Fakhfakh  T, Haddar  M,  Effect of transmission error on the dynamic behaviour of gearbox housing. International Journal of Advanced Manufacturing Technology, 2007, 34(3–4): 211–218
3 Tian  Z, Zuo  M, Wu  S. Crack propagation assessment for spur gears using model-based analysis and simulation. Journal of Intelligent Manufacturing, 2012, 23(2): 239–253
4 Ebersbach  S, Peng  Z. Fault diagnosis of gearbox based on monitoring of lubricants, wear debris, and vibration. In: Wang  Q, Chung  Y W, eds. Encyclopedia of Tribology. New York: Springer, 2013, 1059–1064 
5 Rgeai  M, Gu  F, Ball  A,  Gearbox fault detection using spectrum analysis of the drive motor current signal. In: Kiritsis  D, Emmanouilidis  C, Koronios  A, , eds. Engineering Asset Lifecycle Management. London: Springer, 2010, 758–769
6 Hong  L, Dhupia  J S. A time domain approach to diagnose gearbox fault based on measured vibration signals. Journal of Sound and Vibration, 2014, 333(7): 2164–2180
7 Rafiee  J, Arvani  F, Harifi  A,  Intelligent condition monitoring of a gearbox using artificial neural network. Mechanical Systems and Signal Processing, 2007, 21(4): 1746–1754
8 Sanchez  R, Arpi  A, Minchala  L. Fault identification and classification of spur gearbox with feed forward back propagation artificial neural network. In: Proceedings of the 2012 Andean Region International Conference. Washington, D.C.: IEEE, 2012, 215
9 Barakat  M, Lefebvre  D, Khalil  M,  Parameter selection algorithm with self-adaptive growing neural network classifier for diagnosis issues. International Journal of Machine Learning and Cybernetics, 2013, 4(3): 217–233
10 Yang  B S, Han  T, An  J L. ART-KOHONEN neural network for fault diagnosis of rotating machinery. Mechanical Systems and Signal Processing, 2004, 18(3): 645–657
11 Jiang  Z, Fu  H, Li  L. Support vector machine for mechanical faults classification. Journal of Zhejiang University SCIENCE A, 2005, 6(5): 433–439
12 Jiao  B, Xu  Z. Multi-classification LSSVM application in fault diagnosis of wind power gearbox. In: Zhang  T, ed. Mechanical Engineering  and  Technology.  Berlin:  Springer,  2012,  125:  277–283
13 Kang  Y, Wang  C, Chang  Y. Gear fault diagnosis in time domains by using Bayesian networks. In: Melin  P, Castillo  O, Ramirez  E, , eds. Analysis and Design of Intelligent Systems using Soft Computing Techniques. Berlin: Springer, 2007, 41: 618–627
14 Breiman  L, Friedman  J, Olshen  R,  Classification and regression trees. The Wadsworth and Brooks-Cole statistics-probability series. Boca Raton: Chapman & Hall, 1984
15 Breiman  L. Random forests. Machine Learning, 2001, 45(1): 5–32
16 Criminisi  A, Shotton  J. Classification forests. In: Criminisi  A, Shotton  J, eds. Decision Forests for Computer Vision and Medical Image Analysis. London: Springer, 2013, 25–45
17 Han  X, Yang  B S, Lee  S J. Application of random forest algorithm in machine fault diagnosis. In: Mathew  J, Kennedy  J, Ma  L, , eds. Engineering Asset Management. London: Springer, 2006, 779–784
18 Yang  B S, Di  X, Han  T. Random forests classifier for machine fault diagnosis. Journal of Mechanical Science and Technology, 2008, 22(9): 1716–1725
19 Karabadji  N, Khelf  I, Seridi  H,  Genetic optimization of decision tree choice for fault diagnosis in an industrial ventilator. In: Fakhfakh  T, Bartelmus  W, Chaari  F, , eds. Condition Monitoring of Machinery in Non-Stationary Operations. Berlin: Springer, 2012, 277–283
Related articles from Frontiers Journals
[1] Peng ZHOU, Zhike PENG, Shiqian CHEN, Yang YANG, Wenming ZHANG. Non-stationary signal analysis based on general parameterized time--frequency transform and its application in the feature extraction of a rotary machine[J]. Front. Mech. Eng., 2018, 13(2): 292-300.
[2] Xuefeng CHEN, Shibin WANG, Baijie QIAO, Qiang CHEN. Basic research on machinery fault diagnostics: Past, present, and future trends[J]. Front. Mech. Eng., 2018, 13(2): 264-291.
[3] Zhaohui DU, Xuefeng CHEN, Han ZHANG, Yanyang ZI, Ruqiang YAN. Multiple fault separation and detection by joint subspace learning for the health assessment of wind turbine gearboxes[J]. Front. Mech. Eng., 2017, 12(3): 333-347.
[4] Shoudao HUANG, Xuan WU, Xiao LIU, Jian GAO, Yunze HE. Overview of condition monitoring and operation control of electric power conversion systems in direct-drive wind turbines under faults[J]. Front. Mech. Eng., 2017, 12(3): 281-302.
[5] Houjun SU, Tielin SHI, Fei CHEN, Shuhong HUANG. New method of fault diagnosis of rotating machinery based on distance of information entropy[J]. Front Mech Eng, 2011, 6(2): 249-253.
[6] Lixin GAO, Lijuan WU, Yan WANG, Houpei WEI, Hui YE. Intelligent fault diagnostic system based on RBR for the gearbox of rolling mills[J]. Front Mech Eng Chin, 2010, 5(4): 483-490.
[7] Shaohong WANG, Tao CHEN, Jianghong SUN. Design and realization of a remote monitoring and diagnosis and prediction system for large rotating machinery[J]. Front Mech Eng Chin, 2010, 5(2): 165-170.
[8] Xiaohu CHEN, Wenfeng WU, Hangong WANG, Yongtao ZHOU, . Distributed monitoring and diagnosis system for hydraulic system of construction machinery[J]. Front. Mech. Eng., 2010, 5(1): 106-110.
[9] LI Zhinong, HE Yongyong, CHU Fulei, WU Zhaotong. Blind identification of threshold auto-regressive model for machine fault diagnosis[J]. Front. Mech. Eng., 2007, 2(1): 46-49.
[10] DUAN Li-xiang, ZHANG Lai-bin, WANG Zhao-hui. De-noising of diesel vibration signal using wavelet packet and singular value decomposition[J]. Front. Mech. Eng., 2006, 1(4): 443-447.
[11] LIANG Lin, XU Guang-hua. Reduction of rough set attribute based on immune clone selection[J]. Front. Mech. Eng., 2006, 1(4): 413-417.
[12] HU You-min, YANG Shu-zi, DU Run-sheng. Distributed flexible reconfigurable condition monitoring and diagnosis technology[J]. Front. Mech. Eng., 2006, 1(3): 276-281.
[13] LI Wei-hua, SHI Tie-lin, YANG Shu-zi. An approach for mechanical fault classification based on generalized discriminant analysis[J]. Front. Mech. Eng., 2006, 1(3): 292-298.
[14] YANG Ping. Data mining diagnosis system based on rough set theory for boilers in thermal power plants[J]. Front. Mech. Eng., 2006, 1(2): 162-167.
Full text



  Shared   0